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An Interactive Guide to the Fourier Transform

(betterexplained.com)
247 points pykello | 5 comments | 02 Dec 25 06:50 UTC | HN request time: 0.001s | source
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constantcrying ◴[07 Dec 25 17:49 UTC] No.46183527[source]▶
>The Fourier Transform is one of deepest insights ever made.

No, it is not. In fact it is quite a superficial example of a much deeper theory, behind functions, their approximations and their representations.

replies(1): >>46183967 #
1. fedsocpuppet ◴[07 Dec 25 18:44 UTC] No.46183967[source]▶
The Fourier transform predates functional analysis by a century. I don't see the point in downplaying its significance just because 'duh it's simply a unitary linear operator on L2'.
replies(1): >>46184483 #
2. NewsaHackO ◴[07 Dec 25 19:45 UTC] No.46184483[source]▶
But is it the deepest insights ever made?
replies(1): >>46184930 #
3. badlibrarian ◴[07 Dec 25 20:40 UTC] No.46184930[source]▶
The Fourier Transform isn't even Fourier's deepest insight. Unless we're now ranking scientific discoveries based on whether or not they get a post every weekend on HN.

The FFT is nifty but that's FINO. The Google boys also had a few O(N^2) to O(N log N) moments. Those seemed to move the needle a bit as well.

But even if we restrict to "things that made Nano Banana Pro possible" Shannon and Turing leapfrog Fourier.

replies(1): >>46186141 #
4. lispisok ◴[07 Dec 25 22:52 UTC] No.46186141{3}[source]▶
>Unless we're now ranking scientific discoveries based on whether or not they get a post every weekend on HN.

Glad I'm not the only one who noticed there is a weekly (or more) post on what Fourier transform is.

replies(1): >>46188669 #
5. chemotaxis ◴[08 Dec 25 05:20 UTC] No.46188669{4}[source]▶
It's really getting in the way of all the daily AI opinion pieces I come here to read.

More seriously, there are tens of thousands of people who come to HN. If Fourier stuff gets upvoted, it's because people find it informative. I happen to know the theory, but I wouldn't gatekeep.